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Register a new userNormal-mode Analysis for Collective Neutrino Oscillations
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Sagar Airen
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In an interacting neutrino gas, collective modes of flavor coherence emerge that can be propagating or unstable. We derive the general dispersion relation in the linear regime that depends on the neutrino energy and angle distribution. The essential scales are the vacuum oscillation frequency $omega=Delta m^2/(2E)$, the neutrino-neutrino interaction energy $mu=sqrt{2}G_{rm F} n_ u$, and the matter potential $lambda=sqrt{2}G_{rm F} n_e$. Collective modes require non-vanishing $mu$ and may be dynamical even for $omega=0$ (fast modes), or they may require $omega ot=0$ (slow modes). The growth rate of unstable fast modes can be fast itself (independent of $omega$) or can be slow (suppressed by $sqrt{|omega/mu|}$). We clarify the role of flavor mixing, which is ignored for the identification of collective modes, but necessary to trigger collective flavor motion. A large matter effect is needed to provide an approximate fixed point of flavor evolution, while spatial or temporal variations of matter and/or neutrinos are required as a trigger, i.e., to translate the disturbance provided by the mass term to seed stable or unstable flavor waves. We work out explicit examples to illustrate these points.
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We investigate collective flavor oscillations of supernova neutrinos at late stages of the explosion. We first show that the frequently used single-angle (averaged coupling) approximation predicts oscillations close to, or perhaps even inside, the neutrinosphere, potentially invalidating the basic neutrino transport paradigm. Fortunately, we also find that the single-angle approximation breaks down in this regime; in the full multiangle calculation, the oscillations start safely outside the transport region. The new suppression effect is traced to the interplay between the dispersion in the neutrino-neutrino interactions and the vacuum oscillation term.
In our previous studies (see [1] and references therein) we developed a new theoretical framework that enabled one to consider a new mechanism of neutrino quantum decoherence engendered by the neutrino radiative decay. In parallel, another framework was developed (see [2] and references therein) for the description of the neutrino quantum decoherence due to the non-forward neutrino scattering processes. Both mechanisms are described by the master equations in the Lindblad form. We study the influence of the neutrino quantum decoherence on collective neutrino oscillations. In the present studies we are are not interested in a specific mechanism of neutrino quantum decoherence. Therefore, we use the general Lindblad master equation for the description of the neutrino quantum decoherence and do not fix an analytical expressions for the decoherence and relaxation parameters.
Neutrino oscillations in a hot and dense astrophysical environment such as a core-collapse supernova pose a challenging, seven-dimensional flavor transport problem. To make the problem even more difficult (and interesting), neutrinos can experience collective oscillations through nonlinear refraction in the dense neutrino medium in this environment. Significant progress has been made in the last decade towards the understanding of collective neutrino oscillations in various simplified neutrino gas models with imposed symmetries and reduced dimensions. However, a series of recent studies seem to have reset this progress by showing that these models may not be compatible with collective neutrino oscillations because the latter can break the symmetries spontaneously if they are not imposed. We review some of the key concepts of collective neutrino oscillations by using a few simple toy models. We also elucidate the breaking of spatial and directional symmetries in these models because of collective oscillations.
Collective neutrino oscillations can potentially play an important role in transporting lepton flavor in astrophysical scenarios where the neutrino density is large, typical examples are the early universe and supernova explosions. It has been argued in the past that simple models of the neutrino Hamiltonian designed to describe forward scattering can support substantial flavor evolution on very short time scales $tapproxlog(N)/(G_Frho_ u)$, with $N$ the number of neutrinos, $G_F$ the Fermi constant and $rho_ u$ the neutrino density. This finding is in tension with results for similar but exactly solvable models for which $tapproxsqrt{N}/(G_Frho_ u)$ instead. In this work we provide a coherent explanation of this tension in terms of Dynamical Phase Transitions (DPT) and study the possible impact that a DPT could have in more realistic models of neutrino oscillations and their mean-field approximation.
Collective neutrino oscillations play a crucial role in transporting lepton flavor in astrophysical settings, such as supernovae, where the neutrino density is large. In this regime, neutrino-neutrino interactions are important and simulations in mean-field approximations show evidence for collective oscillations occurring at time scales much larger than those associated with vacuum oscillations. In this work, we study the out-of-equilibrium dynamics of a corresponding spin model using Matrix Product States and show how collective bipolar oscillations can be triggered by quantum fluctuations if appropriate initial conditions are present. The origin of these flavor oscillations, absent in the mean-field, can be traced to the presence of a dynamical phase transition, which drastically modifies the real-time evolution of the entanglement entropy. We find entanglement entropies scaling at most logarithmically in the system size, suggesting that classical tensor network methods could be efficient in describing collective neutrino dynamics more generally.
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